This work presents, for the first time, a dual time stepping (DTS) approach to solve the global system of equations that appears in the hybridisable discontinuous Galerkin (HDG) formulation of convection-diffusion problems. A proof of the existence and uniqueness of the steady state solution of the HDG global problem with DTS is presented. The stability limit of the DTS approach is derived using a von Neumann analysis, leading to a closed form expression for the critical dual time step. An optimal choice for the dual time step, producing the maximum damping for all the frequencies, is also derived. Steady and transient convection-diffusion problems are considered to demonstrate the performance of the proposed DTS approach, with particular emphasis on convection dominated problems. Two simple approaches to accelerate the convergence of the DTS approach are also considered and three different time marching approaches for the dual time are compared.

这项工作首次提出了双时间步长（DTS）方法，以解决对流扩散问题的可混合不连续伽勒金（HDG）公式中出现的整体方程组。给出了带有DTS的HDG全局问题的稳态解的存在性和唯一性的证明。DTS方法的稳定性极限是使用冯·诺依曼（von Neumann）分析得出的，从而导致关键的双重时间步长的闭合形式表示。还推导出了双时间步长的最佳选择，即为所有频率产生最大阻尼。稳态和瞬态对流扩散问题被认为可以证明所提出的DTS方法的性能，特别是对流占优的问题。